Verification of numerical methods and mathematical model developed for simulation of radionuclides migration in natural disperse environments

Simulation of radionuclides vertical migration was successfullyimplemented in the first versions of SPS  (Simulation  of  Processes  in  Soil)  software  and  was  based  on a  numerical  solution  of  the  mathematical model  of  interconnected  heat  and  moisture  transfer  in  one  dimension.  But  in  order  to  solve  problems  of  a comprehensive assessment of the state of the biosphere under radionuclides pollution and better approximation of simulation results to real processes, authors developed SPS v2.0 software. One of the modules of SPS v2.0 uses  new  mathematical  model  that  describes  the  spatial  migration  of  radionuclides  in  soil  (3D-model). The numerical solution of this mathematical model is based on the application of the finite element method and the  analytical  approximation  of  thermal  conductivity  and  liquid pressure  coefficients.  Such  approach  makes possible  to  use  parallel  computing  technologies  for  simulation. The  mathematical  model  used  in  SPS  v2.0, as well as numerical methods forsolving it, require verification, which is carried out in this article. Verification of the developed numerical methodswas carried out using ComsolMultiphysics software and SPS v2.0 module with the following comparison of the calculation results. The difference in the calculation results obtained using the listed software is less than 5 %, therefore, the numerical methods are correctly implemented in SPS v2.0 and have a solution accuracy comparable to the numerical methods used in modern software. For the mathematical model  verification  were  used  the  results  of  experimental  measurements  of  meteorological  conditions, distribution  of  moisture  and  temperature  in  soil,  which  were  compared  with  the  simulation  results  obtained in SPS v2.0. The comparison shows that the error in the calculation of the analyzed parameters does not exceed 5 %, which allows the developed model to be used for solvation of practical problems in the subject area.

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